On endomorphisms of free groups that preserve primitivity

被引：14
作者：
Ivanov, SV [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
ARCHIV DER MATHEMATIK | 1999年 / 72卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s000130050309
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proven that if phi is an endomorphism of a free group F-n = < x(1),...,x(n)> of rank n such that phi(u) is primitive whenever so is u is an element of F-n and phi(F-n) contains a primitive pair (i.c., a pair alpha(x(1)), alpha(x(2)) with alpha is an element of Aut F-n), then phi is an automorphism. Also, every endomorphism of F-2 that preserves primitivity is an automorphism.
引用
收藏
页码：92 / 100
页数：9
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